fundamental design tradeoff and performance …...群馬大学 小林研究室 gunma university...
TRANSCRIPT
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群馬大学 小林研究室
Gunma University Kobayashi Lab
Fundamental Design Tradeoff and Performance Limitation of Electronic Circuits
Based on Uncertainty Relationships
H. Kobayashi I. Shimizu N. TsukijiM. Arai K. Kubo H. Aoki
Gunma University Oyama National College of TechnologyTeikyo Heisei University
SC4-1 13:30-14:00 Oct. 27, 2017 (Fri)
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My First Research
Computer with Superconductor (Josephson Device)
Under supervision of Prof. Ko Hara (原 宏)at University of Tokyo
Physicist
Undergraduate (Bachelor) course, 4th year
[1] K. Hara, H. Kobayashi, S. Takagi, F. Shiota, “Simulation of a Multi-Josephson Switching Device'', Japanese J. of Applied Physics (1980).
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Research Motivation of This Paper
time
Quantum state 1
Quantum state 2
ΔE
Δt
ΔE Δt ≥ h/(4π) Uncertainty principle
Transition time Δt Time uncertainty
My strong impression :
State transition
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Our Statement
Uncertainty relationships are everywhere in electronic circuits
Ultimately, some would converge to Heisenberg uncertainty principle
in quantum physics.
陰陽思想太極図
Our conjecture
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Contents
● Research Objective
● Uncertainty Principle and Relationship
● Invariant Quantity
● Electronic Circuit Performance Analogyto Uncertainty Relationship and Invariant
● Waveform Sampling Circuit
● Conclusion
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Contents
● Research Objective
● Uncertainty Principle and Relationship
● Invariant Quantity
● Electronic Circuit Performance Analogyto Uncertainty Relationship and Invariant
● Waveform Sampling Circuit
● Conclusion
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Research Objective
● Our ObjectiveIn analog electronic circuits- Clarify tradeoff among their performance indices - Provide their fundamental limitation
● Our ApproachBased on- Uncertainty principle in quantum mechanics- Uncertainty relationship in signal processing
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Contents
● Research Objective
● Uncertainty Principle and Relationship
● Invariant Quantity
● Electronic Circuit Performance Analogyto Uncertainty Relationship and Invariant
● Waveform Sampling Circuit
● Conclusion
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Uncertainty Principle in Quantum Mechanics
Δx Δp ≥ h/(4π)
Δt ΔE ≥ h/(4π)
These cannot be proved principle.
x: position, p: momentum.
t: time, E: energy
W. K. Heisenberg
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Uncertainty Relationship in Signal Processing (1)
Sampling frequency : fsSampling period: Ts (= 1/fs)
Δf = fs/N = 1/(Ts N)
Δf Ts = 1/N
● Discrete Fourier Transform (DFT)
Number of DFT points :N
Time & frequency resolution
This can be proved mathematically Relationship
frequencyΔf
0
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Uncertainty Relationship in Signal Processing (2)
● Uncertainty Relationship between Time & Frequency of Continuous Waveform
This can be proved mathematically Relationship
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Contents
● Research Objective
● Uncertainty Principle and Relationship
● Invariant Quantity
● Electronic Circuit Performance Analogyto Uncertainty Relationship and Invariant
● Waveform Sampling Circuit
● Conclusion
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Importance of Invariant (1)
・Energy conservation law・Mass conservation law・Momentum conservation law・Charge conservation law
Invariant quantity clarify phenomena & characteristics
Conservation Law in Physics :
vmv2v1 m2m1 m1 m2
p1 = m1 v1, p2 = m2 v2 p1’= m1 vm, p2’=m2 vm
p1+ p2 = p1’ + p2’13/50
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Importance of Invariant (2)Invariant quantity
clarify phenomena & characteristics
f(x) = x
Fixed-Point in Mathematics :
Compass Polaris
Utility for Voyage
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Contents
● Research Objective
● Uncertainty Principle and Relationship
● Invariant Quantity
● Electronic Circuit Performance Analogyto Uncertainty Relationship and Invariant
● Waveform Sampling Circuit
● Conclusion
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Gain, Signal Band and Power
● For a given amplifier
Gain ・ bandwidth = constant
Gain → large, bandwidth → narrow
PowerGain ・ Bandwidth
FOM = Technology constant
● Amplifier Performance
→ Converge to uncertainty principle
conjecture
Gai
n [
dB
]
Frequency [Hz]
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ADC Sampling Speed, Resolution and Power
Resolution: Vfull /ΔV = 2n
FOM = Δt・ΔV・P / Vfull
= Δt・P / 2n
Power: P
Sampling period: Δt FOM =
Voltage Resolution・PowerSampling Speed
FOM → Smaller, ADC → Better
Technology constant
→ Converge to uncertainty principleconjecture 17/50
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Clock Jitter, Power
Δt ・E ≥ K1
Clock jitter: Δt
Clock generator energy : Epower : P
Design tradeoff
(Δt / T ) P ≥ K1
T
Power → larger, Jitter → smaller
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Noise, Capacitor
p (momentum) ⇔ Q (charge)
v (velocity) ⇔ V (voltage)
m (mass) ⇔ C (capacitor)
Momentum conservation law⇔ Charge conservation law
Uncertainty principleΔx Δp ≥ K ⇔ ΔV f ΔQ ≥ K
⇔ C ΔV2 f ≥ K
ΔV2 = kT/CNoise power
Noise bandwidth: f
Analogy
C → large, Noise → small 19/50
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Noise, Capacitor (2)
Vout(t)
R
+ +
--
C
Transfer function
G(s) = 1/ (1 + sRC )
Vin(t)
Ec = (1/2) C Vout
● For a given T=RCthe same gain & phase characteristics for different (R1, C1), (R2, C2), …with R1 C1 = R2 C2 = … = T
Vnoise = kT/ C
● For a given Vout
2
2
C → large, R → smallSame gain & phase characteristicsLow noiseLarge energy
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Capacitor Charge & Loss
I
Vout
C
R
Eloss = (R・I )・I・T= R・C・V・I
Vout = I・T / C
Eloss
Eloss ・T= R・C・Vout
For given R, C, Vout
I → small, T → long Eloss → small
Uncertainty relationship
I : Charge CurrentT: Charge Duration
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Analog Electronic Circuits
Δa Δb ≥ K
Performance tradeoffs are everywhere in circuits
Δa Δb = K K: Technology constant
For a given technology
Technology → advance K → smaller
● In some cases, these can be proved. Uncertainty relationship
● In other cases, these can NOT be proved.
Conjecture: this converges to uncertainty principle22/50
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Analog Circuit and Quantum Mechanics
Myth- Real world signals → analog- Computer world signals → digital.
Truth- quantum mechanics →
signals in nature → digital (discrete).
- Current → average of electrons’ moves- Electronic noises → their variation.
Conjecture- Analog electronic circuit performance
→ Limited by quantum mechanics23/50
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Analogy
p (momentum) ⇔ Q (charge)
v (velocity) ⇔ V (voltage)
m (mass) ⇔ C (capacitor)
Momentum conservation law⇔ Charge conservation law
Analogy
In Physics, analogy is just a coincidence,NOT inevitable.
Difference
Any connection of m1 & m2 > m1, m2
Series connection of C1 & C2 < C1, C2
m2m1
C1 C224/50
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Bridge Through Plank Constant
“Mehr Licht !”
by J. W. von Goethe
“Let there be light !”
Old testament
Energy in the light: E = (h/(2π)) ω
ΔE Δτ ≥ h/(4π)
Uncertainty Principle
Δω Δτ ≥ 1/2
(h/(2π)) Δω Δτ ≥ h/(4π)
Uncertainty RelationshipAnalogy to Principle
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Measurement and Simulation
Measurement : Active, Passive
Active: Stimulus DeviceResponse MeasuredDevice state Disturbed.
Passive: No stimulusDevice state Not disturbed.
Uncertainty principleall measurements disturb device state.
Circuit simulation No disturbance.
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Contents
● Research Objective
● Uncertainty Principle and Relationship
● Invariant Quantity
● Electronic Circuit Performance Analogyto Uncertainty Relationship and Invariant
● Waveform Sampling Circuit
[2] M. Arai , H. Kobayashi , et. al.,“Finite Aperture Time Effects in Sampling Circuit,”IEEE 11th International Conference on ASIC, Chengdu (Nov. 2015).
Example ofUncertainty RelationshipIn Signal Processing
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Waveform Sampling
- Finite aperture time (non-zero turn-off time)- Aperture jitter
time
― analog signal
● Sampled point
suffers from
volt
age
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Sampling Circuit
29
時間
電圧
時間
電圧
時間
電圧
時間
電圧
CSW
Vin Vout
CSW
Vin Vout
CSW
Vin Vout
• SW: ON
•Vout(t) = Vin(t)
Track mode
•SW: OFF
•Vout(t) = Vin(tOFF)
Hold mode
Track Hold
time
time
timetime
volt
age
volt
age
volt
age
volt
age
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Finite Aperture Time
30
時間
電圧
時間
電圧
CSW
Vin Vout
CSW
Vin Vout
• SW: ON
•Vout(t) = Vin(t)
Track mode
•SW: OFF
•Vout(t) = Vin(tOFF)
Hold modetime
time
volt
age
volt
age
Finite transition time from track to hold modes
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Analogy with Camera Shutter Speed
Camera: Finite Shutter Speed Sampling Circuit:Finite Aperture Time
Moving Object
Blurred
Input signal
Acquired signal
High frequency
Low pass filtered
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Signal Frequency and Aperture Time
Higher frequency signal ⇒ More affected by finite aperture time
HT
time
time
Low frequency
Aperture time
HT
time
time
High frequency
Aperture time
Inp
ut
volt
age
Inp
ut
volt
age
Ou
tpu
t vo
ltag
e
Ou
tpu
t vo
ltag
e
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VgVinVc
Transfer Function Derivation
Track Hold Circuit
+
-
Voltage
Time
Obtain values of ●
Equivalent time sampling
Obtain gain, phase for each frequency
Frequency transfer function
SW
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Derived Transfer Function
Transfer function in case of finite aperture time
Track Hold Circuit
+
-
SW
τ1 = R C
[3] A. Abidi, M. Arrai, K. Niitsu, H. Kobayashi, “Finite Aperture Time Effects in Sampling Circuits,”24th IEICE Workshop on Circuits and Systems, Awaji Island, Japan (Aug. 2011)
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Consistency with Zero Aperture Time Case
Transfer function in case of finite aperture time
Transfer function in case of zero aperture time
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τ1, τ2 Effects to Bandwidth
τ1 (= R C)
τ2 (aperture time) : varied: fixed
Bandwidth starts to decrease at τ2 / τ1= 1
τ1, τ2 effects to bandwidth are comparable.
Numerical calculation from the derived transfer function
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VgVinVc
SPICE Simulation Verification
Track Hold Circuit
+
-
Voltage
Time
Obtain values of ●
Equivalent time sampling
Obtain gain, phase for each frequency
Frequency transfer function
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00.50.711.5234567
τ2[ns]0351015202530354050
τ2[ns]
SPICE Simulation Conditions
Results
SPICE Simulation Results
Gai
n [
dB
]
ω [rad/s]
Theory (Derived Transfer Function)
ω [rad/s]
Gai
n [
dB
]
Results
+
―
TSMC 0.18um
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simulationtheory
Comparison of -3dB Bandwidth
W=20um
ω(-
3d
B)[
rad
/s]
14
12
0
2
4
6
8
10
0 5 1510τ2[ns]
simulationtheory
W=200um
ω(-
3d
B)[
rad
/s]
20
16
0
4
8
12
τ2[ns]0 10 504020 30
ω(-
3d
B)[
rad
/s]
simulationtheory
W=2um
τ2[ns]0 10 504020 30
35
30
0
5
10
15
20
25
Large discrepancies !
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NMOS ON-Conductance Nonlinearity
Effective aperture time
W=20um
1/R
on
[S]
4
3
0
1
2
Vg[V]0 0.5 2.01.0 1.5
W=2um
1/R
on
[S]
4
3
0
1
2
Vg[V]0 0.5 2.01.0 1.5
W=200um
1/R
on
[S]
4
3
0
1
2
Vg[V]0 0.5 2.01.0 1.5
○ region
Strong nonlinearity of 1/Ron
Define effective aperture time
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ON-Conductance and Effective Aperture Time
Region Effective aperture time
1/R
on
(lo
g sc
ale
) [S
]
Vg [V]
200um
20um
2um
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Empirical Effective Aperture Time Derivation
BA
0.43
Vg[V]0 0.5 2.01.0 1.5
1/R
on
(lo
g sc
ale
) [S
]
20um
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simulation*0.44/1.8theory
ω(-
3d
B)[
rad
/s]
τ2[ns]
20
0
5
10
15
0 5 1510τ2[ns]
ω(-
3d
B)[
rad
/s]
1412
02468
10
0 5 1510 τ2[ns]
ω(-
3d
B)[
rad
/s]
3530
05
10152025
0 5 1510
simulation*0.43/1.8theory
simulation*0.37/1.8theory
simulationtheory
simulationtheory
simulationtheory
Discussion AgainW=20um W=2umW=200um
τ2[ns]
ω(-
3d
B)[
rad
/s]
20
0
5
10
15
0 20 403010
X 0.44/1.8X 0.37/1.8 X 0.43/1.8
0 5 1510
ω(-
3d
B)[
rad
/s]
1412
02468
10
τ2[ns]
ω(-
3d
B)[
rad
/s]
3530
05
10152025
τ2[ns]0 20 403010
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simulation*0.44/1.8theory
simulation*0.43/1.8theory
simulation*0.43/1.8theory
simulation*0.37/1.8theory
Various Values for RC, W
200um 20um
20um 2um
R=50Ω, C=10pF
R=50Ω, C=0.1pF
τ2[ns]
ω(-
3d
B)[
rad
/s]
20
0
5
10
15
0 4 1062 8
ω(-
3d
B)[
rad
/s]
15
0
5
10
τ2[ns]0 5 1510
τ2[ns]
ω(-
3d
B)[
rad
/s]
15
0
5
10
0 0.5 1.51.0τ2[ns]
ω(-
3d
B)[
rad
/s]
3530
05
10152025
0 0.5 1.51.0
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Trade-off of Time Constant and Bandwidth
Time
Short
Long
Wide
Narrow
Aperture time Bandwidth
RC time constant and bandwidth Aperture time and bandwidth
Band
RC bandwidth
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Summary
● Derived explicit transfer function of sampling circuit with finite aperture time effect.
● Verified it with SPICE simulation
● Introduced concept of effective finite aperture time
● Showed uncertainty relationship between time constants and bandwidthin sampling circuit.
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Contents
● Research Objective
● Uncertainty Principle and Relationship
● Invariant Quantity
● Electronic Circuit Performance Analogyto Uncertainty Relationship and Invariant
● Waveform Sampling Circuit
● Conclusion
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Conclusion
Analog electronic circuit
● Its design tradeoff as well as FOM
Explained with
Analogy to uncertainty principle/relationship.
● Uncertainty principle and relationship
Its ultimate performance limitation
Our strong belief:
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Final Statement
大道以多岐亡羊,學者以多方喪生(列子)
Current status of circuit design and analysis area
We need to establish a unified theory for circuit design and analysis area.
Only individual techniques have been developed.
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Thank you for listening
謝謝
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